AE_LE_crack

An analytic element for intersecting cracks in a linear elastic half-space. A program which calculated the stress field for given number of cracks, which may intersect, in a uniform stress field. The input files for the plot properties and the physical constants are provided through the MATLAB program run_ae_master.m which then calls the program run_AE_LE_master.exe to solve and plot the solution.

The program includes the Cartesian stress field ( , & ), the principal stress field ( , & ) and the principal stress trajectories. Also, it computes the displacement filed and the displacement trajectories. For a given resolution and coordinates. The results are saved as a .mat-file as simulation_[todays date]_[version].mat, the program automatically save as the current date and assigns the version.

This program has been developed using MATLAB and Microsoft Visual Stuido; only the .m-, .cpp- and .exe-files are included in the repository. The solution also uses the Eigen library (Guennebaud & Jacob, 2010).

Instructions

The plots are generated using the MATLAB program run_ae_master.m. The script calls the C++ program which solves the system and plots the results. To run the program simply run the MATLAB script.

Input data

This list contains all the definitions of the user input data defined in run_ae_master.m. These are the model properties:

• nu the Poisson's ratio
• sigma_11inf the uniform stress state
• z1 starting coordinates for cracks
• z2 end coordinates for cracks
• p vector for pressures of the cracks
• ma number of coefficients to sovle
• Na number of interation points along the cracks

These are the plotting properties:

• xfrom the starting value for x-axis
• xto the end value for the x-axis
• yfrom the starting value for the y-axis
• yto the end value for the y-axis
• Nx the number of grid points in the x-diraction
• Ny the number of grid points in the y-direction
• Ntraj the number of steps for the stress trajectories
• lvs_traj the number of stress trajectories
• xtraj the vector containing the start and end point for the line hwere the trajectores are evenly spaced, for
• ytraj the vector containing the start and end point for the line hwere the trajectores are evenly spaced, for
• Nw the number of grid points in the x- and y-direction for the displacements

Plotting functions

The following functions are included for the plotting scheme in MATLAB

• creat_figure.m creat the figure window
• Plot_line.m plots a line from z1 to z2

Citations

The program has been used in the following paper:

• Comming soon.

References

Guennebaud, G., Jacob, B., et al. (2010). Eigen v3. http://eigen.tuxfamily.org.